To determine which line is perpendicular to a line with a given slope, we need to find the slope of the perpendicular line. The slope of a line perpendicular to another is the negative reciprocal of the original slope.
Let's follow the steps to solve this:
1. Identify the given slope:
The given slope of the original line is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the negative reciprocal:
The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
Taking the negative of this reciprocal, we get [tex]\(\frac{6}{5}\)[/tex].
3. Interpret the result:
The slope of a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
So, the line that is perpendicular to the line with slope [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex]. Therefore, any line that has this slope, such as perhaps line PQ if it represents this scenario, will be the line perpendicular to the original.
